What is ln(x)+5ln(y)-3ln(z) ?

The solution to ln(x)+5ln(y)-3ln(z) is ln((xy^5)/(z^3))

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simplify ln(x)+5ln(y)-3ln(z)

simplify

ln (x) + 5 ln (y) - 3 ln (z)

ln (\frac{x y ^{5}}{z ^{3}})

Solution steps

ln (x) + 5 ln (y) - 3 ln (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

5 ln (y) = ln (y^{5})

= ln (x) + ln (y^{5}) - 3 ln (z)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (x) + ln (y^{5}) = ln (x y^{5})

= ln (x y^{5}) - 3 ln (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (z) = ln (z^{3})

= ln (x y^{5}) - ln (z^{3})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (x y^{5}) - ln (z^{3}) = ln (\frac{x y ^{5}}{z ^{3}})

= ln (\frac{x y ^{5}}{z ^{3}})

lo g_{10} (1000 x) - lo g_{10} (\frac{200}{x})

lo g_{3} (x) - 2 lo g_{3} (x)

lo g_{10} (\frac{2 x}{3 y})

ln (e x)

ln (\frac{2 - x}{x})

What is ln(x)+5ln(y)-3ln(z) ?
The solution to ln(x)+5ln(y)-3ln(z) is ln((xy^5)/(z^3))